Question

A stone is dropped into a quiet lake and waves move in circles at a speed
of 4cm per second.
At the instant, when the radius of the circular wave is 10 cm, how
fast is the enclosed area increasing?

Answer 1

@Noemi95 @Shannon20150 @9 @terenzreignz

Answer 2

IF the waves move at 4cm per second, then the radius of the circles also increase 4cm per second... namely
\[\Large \frac{dr}{dt}=4\]

Answer 3

Thank you sir

Answer 4

Enclosed area =
\[\huge A=\pi r^2\]

We want...
\[\huge \frac{dA}{dt}=\frac{dA}{dr}\times \frac{dr}{dt}\]

Answer 5

You can also just differentiate A=pi r^2 implicitly w.r.t. t since you know dr/dt.

\[\Large A=\pi r^2\]
\[\Large \frac{ dA }{ dt} = 2 \pi r \frac{ dr }{ dt}\]